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Design Considerations – Solar PV Array

String Sizing

String sizing is the first step in designing the PV array. It is primarily about matching string voltages to the inverter input operating window. This has long-reaching effects on the whole solar energy system, from the ease of installation, labor and material costs, and performance.

In determining the optimum number of modules in a string, there are actually three inverter input parameters that we should meet with our array voltages:

  • · Minimum Input Voltage – this is the minimum input voltage that must be met before the inverter starts to get DC power from the PV array for conversion to AC. The whole system will stop producing power once the array voltage goes lower than this value. This is a common cause of performance issues for solar systems. The PV array’s operating voltage, even if designed by a solar PV engineer, can go below this minimum input voltage if he has failed to consider the effect of temperature on PV module voltages. Another reason why PV strings sometimes fail to meet the minimum input voltage is when the grid voltage increases by a percentage, the minimum input voltage also increases by the same percentage. Other than these reasons, the PV modules also degrade over time, usually around 0.8% of the rated power per year. This corresponds to an estimated voltage loss of 0.4% per year or 10% over the course of its 25-year lifespan.

  • · Maximum Input Voltage – this determines the maximum DC voltage that the PV array can have. The inverter can be damaged if exposed to voltages higher than this value. A common cause of overvoltage to the inverter is mistakenly putting two strings in series rather than in parallel. Similar to the minimum input voltage, the PV array can also accidentally go above this maximum input voltage if the solar PV engineer fails to consider temperature effects. PV modules’ voltage increases with decreasing temperature. In most cases, the temperature variation from standard temperature (25OC) to the lowest site temperature is much more than the variation to the highest site temperature, especially for locations that experience winter. This means that the effect of voltage increase due to decreasing temperature will be much more than the effect of voltage decrease due to increasing temperature.

  • · MPP Voltage Range – this is the voltage range of the string in which the inverter can track the MPP of the PV modules. Fortunately for designers, if the string is designed so that its operating voltage will always be within the maximum and minimum input voltages, its VMPP will also most likely fall in the MPP voltage range.

Case Study: DC Voltage Calculations in String Sizing

This case study illustrates the step by step process in string sizing for solar energy systems.

Location: Springfield, Massachusetts.

PV module: Yingli YL230P-29b, 230 W STC, 29.5 VMP, 7.8 IMP, 37.0 VOC, 8.4 ISC, -0.137 V/°C temperature coefficient of VOC (-0.37%/°C x 37.0 VOC), -0.133 V/°C temperature coefficient of VMP (based on the published temperature coefficient for Pmp, -0.45%/°C x 29.5 VMP).

Inverter: SMA STP25000-TL, 25 kW, 1,000 Vdc maximum input, 188V start input voltage.

We first need to determine the highest and lowest expected temperature in our location. We can get this data from NASA’s web mapping application, POWER. This can be accessed on this link:

  • Scroll down to the Multiple Data Access Options part and click on Power Data Access Viewer:

  • On Choose a User Community, just keep it at SSE-Renewable Energy.

  • On Choose a Temporal Average, choose Climatology.

  • On Enter Lat/Lon or Add a Point to Map, you can point the location on the map or enter the location’s latitude and longitude.

  • The Select Time Extent Part is not needed.

  • Keep ASCII selected on the Select Output File Formats.

  • Scroll down on the POWER Single Point Data Access window to number 6, Select Parameters. Double click on the Meteorology (Temperature) folder to expand it and check on Maximum and Minimum Temperatures at 2 meters.

  • On the bottom of this window, click Submit.

  • It will take you to another window. On the Output files, click ASCII.

  • It will open another tab that looks like the one shown below. We will be able to see on the bottom part, the maximum and minimum expected temperatures for each month. On this site, our lowest expected temperature is -10.08OC which will occur in January while the highest is 26.82OC in August.

Maximum modules in series – to determine the maximum number of PV modules in series, first calculate the per-module maximum voltage as follows:

where: αVOC = temperature coefficient of VOC

For our example:

VMAX = 37.0V + ((-10.08OC - 25OC) * -0.37%/ OC)

= 37.0V + ((-35.08OC) * -0.37%/ OC)

= 37.0V + (12.9796%)

This means that our VOC of 37.0V will be increased by 12.9796%. This is equivalent to 4.8V.

= 37.0V + 4.8V

VMAX = 41.8V

Then, divide the maximum inverter input voltage by the temperature-corrected open-circuit voltage and round down to the nearest whole number to determine the maximum number of PV modules in series.

NMAX = 1,000V/41.8V